Integral Points on Hyperelliptic Curves
Number Theory
2010-03-17 v4
Abstract
We give a completely explicit upper bound for integral points on (standard) affine models of hyperelliptic curves, provided we know at least one rational point and a Mordell-Weil basis of the Jacobian. We also explain a powerful refinement of the Mordell--Weil sieve which, combined with the upper bound, is capable of determining all the integral points. Our method is illustrated by determining the integral points on a two genus 2 hyperelliptic curves with Mordell--Weil Jacobian ranks of 3 and 6.
Cite
@article{arxiv.0801.4459,
title = {Integral Points on Hyperelliptic Curves},
author = {Y. Bugeaud and M. Mignotte and S. Siksek and M. Stoll and Sz. Tengely},
journal= {arXiv preprint arXiv:0801.4459},
year = {2010}
}